Triangtjlation apparatus for deter



y 1948. E. VON SEGEBADEN 2,445,546

TRIANGULATION APPARATUS FOR DETERMINING THE PATH OF AN AERIAL TARGET Filed June 26, 1944 4 Sheets-Sheet l July 20, 1948. E. VON SEGEBADEN 2,445,546

TRIANGULATION APPARATUS FOR DETERMINING THE PATH OF AN AERIAL TARGET Filed June 26, 1944 4 Sheets-Sheet 2 July 20, 1948. E. VON SEGEBADEN 2,445,546

TRIANGULATION APPARATUS FOR DETERMINING THE PATH OF AN AERIAL TARGET Filed June 26, 1944 4 Sheets-Sheet 3 July 2@, 1 4 E. VON SEGEBADEN 2,445,546

TRIANGULATION APPARATUS FOR DETERMINING THE PATH OF AN AERIAL TARGET Filed June 26, 1944 4 Sheets-Sheet 4 Patented July 20, 1948 STATES ATENT OFFICE Ernst von Segebaden, Drottningholm, Sweden,

assignor to Arenco Aktiebolag,

Stockholm,

Sweden, a Swedish joint-stock company Application June 26, 1944, Serial No. 542,180 In Sweden J uiy 3, 1943 2 Claims.

This invention relates to improvements in apparatus for computing the length of one of the catheti of a right triangle in dependence of variations of the angle between said cathetus and the hypothenuse, for use in fire control instruments for antiaircraft guns for ascertaining the path of an aerial target, whereby the cathetus ascertained denotes the horizontal component of the line of sight to the target. Another object of the invention consists in the provision of improved means for automatically ascertaining the length of said horizontal components even at relatively acute angles of elevation of the line of sight to the target.

In the accompanying drawings:

Fig. l is an elementary diagram in three dimensions illustrating trigonometrically the main principle involved in the invention, especially when adapted for plotting graphically in a fire control instrument the course of an aerial target to predict the point of impact when firing at said target;

Fig. 2 is a diagrammatic perspective view of certain details of an arrangement for determining and plotting the course of the target;

Fig. 3 is an elevational view, partly in section, of part of the fire control instrument provided with the arrangement as illustrated in Fig. 2;

Figs. 4 and 5 illustrate diagrammatically certain improvements of part of the arrangement as shown in Fig. 2;

Fig. 6 shows an arrangement of apparatus embodying the invention and the general plan on which various components of mechanisms are interconnected or cooperate, respectively.

Fig.. 7 is a diagram illustrating the theory of the operation of the device as shown in Fig. 6.

Referring first to Fig. l of the drawings, the course of the aerial target F is ascertained by plotting said course on a horizontal image plane A. The line of sight LF from the observing point L to the target F intersects the image plane A at the point P. Assuming that the target flies at a straight-course at constant speed and altitude the point P moves on the image plane in a straight line which represents the course of the target and is parallel with said course. The height of the image plane A above the point L is indicated by ho.

The displacement of the point P on the image plane A is determined by variations of the bearing angle sv and the altitudinal angle hv of the target. Thus the position of the point P is defined by the length of the co-ordinate p, the distance of the point P from a predetermined point,

2 e. g. a centre C, and by the angle sv between th co-ordinate p and a predetermined line of origin CD. The length of the co-ordinate 1) depends merely on the length of the vertical line'CL 'per pendicular to the image plane A, viz. the, height ho and the altitudinal angle hv of the lineoi sight LF. Hence For the purpose of tracing the course of the target on the image plane A, said plane is turned about its centre proportionally to the angle 8v but in a direction opposite to the azimuthal deflection of the line of sight, and simultaneously the point P represented by the point of a stylus 2 is displaced along a straight radial path into positions given by the formula p=ho.cot hv. Thus on the image plane the line CD is turned whilst the direction of the line CP which contains the stylus 2 is invariable.

The mechanical means for plotting the course of the target F is shown in Figs. 2 and 3. The stylus 2 is mounted on a rod 3 provided with a roller 4. The rod 3 is guided in steady brackets 5 so that it can move rectilinearly only and the roller 4 engages in a spiral groove 6 of a rotary cam disc I the centre of rotation of which is positioned in a line with C and L. The cam disc 1 is secured to a rotary shaft 8 which is turned proportionally to the altitudinal angle hv, measured by a sighting instrument positioned in the observing point L and adjusted to the target, I.

It will first be assumed that the curvature of the groove 6 is determined by the formula in which the angle of rotation of the cam disc 1 from an angular position of origin is. denoted by g). It is, furthermore, assumed that the cam disc turns through an angle equal to the decrement of the altitudinal angle hv and that the center lines of the stylus 2 and the roller 4 are collinear, i. e. that 12:1.

Thus, p=ho.tan =ho.00t lh/u- But then the pitch of the spiral will be too great, when hv is small so that the displacement of the rod 3 will, due to frictional resistance, be made dimcult or rather impossible. To obviate this, a gear ratio is provided between the sighting instrument ,at L and the shaft 8 so that a certain variation of the altitudinal angle lhv renders a greater variation of the angle of rotation of the cam disc. If the ratio of the increment of the angle and s the corresponding decrement of the angle hv is denoted by k (greater than 1) Thus,

2 =ho.cot ho If Ja -4, for instance, each variation of the altitudinal angle hv through 1 will correspond to a rotation through 4 of the cam disc I, so that a complete revolution of the cam disc would theoretically be utilized for adjustment when the altitudinal angle varies from to 90". Figs. 4 and illustrate the relation between the curves not reduced and those reduced as mentioned above.

The above-mentioned formulae are valid under the presumption that the roller 4 is positioned at the centre of rotation of the cam disc I when ho=90. For constructional reasons this is, however; inconvenient. The inner end of the groove tshouid be located beyond the centre of the disc Tat a distance 7'0 therefrom being the distance between the center lines of the roller 4 and the sh m- Then 'p=r ro andboth the above mentioned iromulas will be modified to respectively, as shown inFig. 4, and p=ho.cot he ifrbdth cases;

* A dise of g'las'sfll positioned above the stylus 2 is 'rotatively journalled about the point C on rollers ill and coated onits bottom face with a layer of noii drying paint engaged by the stylus 2; Said bottom face of the disc ll forms the iiiiageplaiie A o'f the point P. The disc H has circumferentially a toothed rim [2 which meshes with a pinion l3 adapted to adjust the disc into angular positions proportional to the azimuthal rotation of the sighting instrument adjusted to the target F. The stylus 2 is so positioned on the rod 3thatits point is positioned at the centre of rdtation of the disc II when the roller 4 is positionedin the innermost end of the groove 6, via. when he=90. For any value of hv the point "ofth'e stylus 2 will always be positioned by cam disc 1 ata dis'tancefrom C corresponding to the doordinate pot the point P. The disc II is turned simultaneously therewith, so that the stylus 2 will on the lower face of the disc ll plot an image of the pathdf flight of the target F.

A lattice l4 consisting of straight wires 9 clamped between twoamiuiar frames I5 and I6 is positioned above the disc H. The lower frame {l d isrotatablysupported by rollers I1, and the upper tooth'ed frai'ne limeshes with a pinion l8 securedto a rotary shaft 19 which by means of abevel gear 20 is connected to certain mechanisms oi the fire control-instrument, so that the course of the targetis introduced into said mechanism. The shaft [9 andthereby also the lattice are turned by means of a handle 2|, so that the wires '9 of the lattice are directed exactly ldflgitudihally of the image of the path of flight piottedon the disc I L Thereby the directions ofthe Wires 9 relative'to a direction of origin indicat'e'the-c'oiirse of the targetr', and saidcoiirse is by means of the -gear 20 introduced to the above-mentioned mechanisms of the fire control instrument.-

in the embodimentshown in Fig. 6 the roller 4 'asiaeie 4 guided by the groove 6 (the equation of which will be recited hereinafter) has a pin 22 engaging in a fixed rectilinear guide groove 24 of a bar 25 directed toward the centre of rotation of the disc I and further into a recilinear guide groove 26 of a multiplier arm 21 positioned above the bar 25 and pivoted to a pin 28. A carriage 30 is displaceably mounted on a rod 29 above the multiplier arm 21 and is provided with a transversely directed bar 3!. The bar 3| has a rectilinear guide groove 53 which is parallel with the groove 24 and in which there is longitudinally displaceable a rack 32 pivoted to the arm 21 by means of a pin 33 which engages in the guide groove 26 of the arm 21. The rack 32 meshes with a toothed cylinder 34 which meshes with still another rack 35, which may be provided with the stylus 2. Alternatively, the cylinder 34 might be adapted to drive another member of the fire control instrument. A wire 36 parallel to the rack 32 is secured to the carriage 30. An arm 3! is pivotally mounted on a pin 38 and provided with a scale 39 marked in terms that indicate the range of the target, whereby the fulcrum at 38 corresponds to the observing point L. The arm 31 is idly turnable on the pin 38 and engages under the influence of a spring an abutment 51 on a gear wheel 54, so that said arm can be arrestedby a stationary abutment 41 on being turned to a position corresponding to an altitudinal angle hv approaching zero. The arm 2'! and thereby also its guide groove 26 are directed perpendicularly to the guide grooves 24 and 53 when the roller 4 is in itsinnermost position in the guide groove 6, i. e. when hv=90. The shaft 8 of the cam disc 1 and the pin 38 are interconnected by a control shaft 40 by means of worm gears 4| and 42, so that the ratio of angular movement (p of the cam disc I from its position of origin (ho=90) and the swing of the arm 3'! from hu=90 is 74:1. The gear 42 drives the toothed wheel 54, to which the pin 38 and the abutment 5| are secured. The shaft 40 is turned by means of a hand wheel 48, and it is by means of a gear 52 connected to the sighting instruinent 43, whereby the arm 31 is adjusted into the altitudinal angle indicated by the instrument 43. The carriage '30 is displaced on the rod '29 by means of a hand wheel 44 and a gear '45, so that the wire 36 is adjusted into a position corresponding to the ascertained value of altitude '71.. This Value of altitudecorr'esponds to the distance between the wire'36 and the fulcrum at 38 which is equal to the distance between the fulcrum 28 and thel'ine or center of the groove'53. A translucent plate of glass is mounted above the wire 36, and on said plate the positions of the target can be plotted point by point durin the flight, viz. by dotting measured'ranges of the target on said plate right above the range scale 39 of the arm 37, the angular position of which is consecutively adjusted in accordance with hv. Obviously, the distance of each dot from the line 33*13 (denoting a horizontal plane) will correspond to the altitude of the target,but, due to unavoidable personal errors in adjustments of the sighting instrument 43andthe'telemetenthe dots on the plate 55 will possibly not correspond exactly to the positions of the target. Thus, even though the target is movable in a straight path and at a constant altitude the distance of the dots from the lin'e 3B B mightdifier slightly.

Fig. 7' illustrates diagrammatically the mode or operation of the device as-shown in 'Fig. 8 for various altitudes. L andLi denote the fulcrums at: re and 2e, respectively, and A denotes the position of the roller 45 when (p=, i. e. when the angwlarposition of the cam disc I corresponds to Ive- 93. Thus, when hv=90 the points L, L1 and A are positioned on the same straight line in Fig: The line LB in Fig. '7 corresponds to the line 38-3 in Fig. 6. The oblique lines extending fromh and L1 (except. the line LFi) denote angulanpositions of the arms 31 and 2! respectively.-

Assuming that the altitudinal angle hv decreases, the cam disc i will rotate correspond-- ingly i rom its angular position of origin and displace the roller 4 outwardly from its point of originfi by a distance defined by the formula p=k1.ho.cot hv knhutan (p /k The curvature of the groove 6 for obtaining such a displacement might be defined by the formula r=ro+lc1.ho.tan (p/IC.

In this example 701 is not equal to 1 (as assumed in the embodiment described with reference to Figs. 1 to 5"), but it is for constructional reasons less than 1. Of course, this is unimportant with a.

respect. to the result obtained, since a reduction of the coeificient ho will merely signify a reduction of, the size of the groove 6 and not a change of'its shape, which is the sole, factor defining the course of the target.

By this displacement of the roller 4 the arm 2? is by the pin 22 swung outwardly (to the right in Figure 6). The wire 36 is by means of the hand wheel 44 adjusted into a position right above the average of the actual altitude h plotted on the plate 55. Consequently, also the bar 31 will be adjusted transversely into such a position that the center line of the groove 53 and thereby also that of the rack 32 will be positioned at a distance irom the fulcrum at 28 corresponding to. the average of altitude h; plotted on the plate 55. By this transversal adjustment of the bar 3| the pin- 33 will slide in the groove 26 so that the rack 32 is displaced longitudinally in the groove 53 into a position at a distance of p=lc1.h.cot he, fromiits. position of origin (when hv=90 and h=ho). Obviously, the multiplier as now described is, however, not necessary for the tracing of the course of the target, since such tracing can be executed irrespective of the actual value of the constant altitude h of the target provided the linear coordinate r of the spiral groove 6 varies;- in accordance with 9. tan

as described heretofore.

Due to rapid increment of 1' when /lc approaches 90, i. e. when hv approaches nil, the curvature of the groove cannot, however, be defined by tan (p/k when (p exceeds a maximum value corresponding to a minimum value of hv. for then the frictional resistance will first make the conveying of movements from the arm 21 to the rack 32 difficult and thereafter impossible. Furthermore, the dimensions of the apparatus would in such case be too extensive. Therefore, the curvature of the groove 6 is defined by the formula between certain limits corresponding to ho=90 to a.a. is a value elected at will. When hv is smaller than a thecurvature of the groove is; die-- iinediby the formula l 1 in w h R r presents-the constant value As will be hereinafter proved by mathematical demonstration, this, formula. can by means. of. the mechanismshow-n in, Fig. 6 afiord the same rev su1t,,i. e. the-same longitudinal movement ofthe. rack 32. as when using the formula as described, hereinbefore.

When. the decreasing hv passes the value the. arm 31" engages yieldingly the abutment. 41; When hv=a, the arm 21 occupies the angular Q0: sition denoted by the line L1A a of Figure 7. The swing of the arm 2'] continues, however, so that it occupies the position denoted by the line LiAhvl, for instance, corresponding to the alti tudinal angle hvl. Since v h, the radial displacement rt Aim of the rollen niis ICI.R.GOS. hviwhen the: roller 4 moves. the [3011s, tion of. the groove 3. that is defined by:- the. formula By turning the arm 2'! the rack 32 is displaced longitudinally and by its own transversal displacement from its transversal position, of origin corresponding to the altitude h said longitudia nal displacement of the rack- 32 is increased. When hv has: passed a the wire 35 is, however, not. adjusted to correspond to the actual value heat. the altitude but to a fictitious Value of altitude denoted hi, by adjusting the wire towthe. measured range of target P=LF on the scale 39 of arm 31 resting against the abutment 41,-

whereby also the rack-321s adjusted transversely to said fictitious altitude hi. Thus the total longitudinal displacement of the rack 32- will b6.

M g-Rhos: h

h. sin a h h .sin h sin a Thus by swinging the arm 21 in accordance with the cosine law the radial displacement of the roller 4 is relatively little, viz.

so that the longitudinal displacement of the rack 32 caused by turning the arm 21 does not correspond to the actual variation of hv, but this error is compensated thereby that the transversal displacement of the rack 32 is increased correspondingly, so that the total longitudinal displacement of the rack 32 will always be determined by the formula p=lc1.h.cot 714:.

In the operation of the arrangement as described with reference to Fig. 6 the roller 4 is displaced rectilinearly. This arrangement may, however, be modified so that the pin 22 of the roller 4 is stationarily journalled in the arm 21 at a predetermined distance ho from the fulcrum at 28. In such case the guide bar 25 is omitted and the roller 4 moves on a circular path. The rod 32 may, however, also in this case be displaced longitudinally at a velocity determined exactly by the formula p=h.cot ho if the curvature of the groove 6 is modified correspondingly, whereby it will approximately be determined by the formula r=r h .tg%

or V

r=r+h .sin% respectively.

The altitude h may, if desired, be plotted automatically on the translucent plate 55 if e. g. the arm 31 has a longitudinal guide, in which is movable a slider which is operably connected to a range computing means provided with a stylus, thereby being adjustable longitudinally of the arm 31 in dependence of the range of the target ascertained by a telemeter.

I claim:

1. In a fire control instrument for anti-aircraft guns, at primary element movable in dependence upon varying altitudinal angle of an aerial target, a rotatable member having a spiral guide for displacing said primary element, a turnable multiplying member connected to said primary element and having a rectilinear guide, a secondary element pivotally connected to said multiplying member and movable along said rectilinear guide to be displaced in a predetermined direction in dependence upon angular movements of said multiplying member as well as in dependence of its movements along'said rectilinear guide, an image plane for recording altitudes of the target, a range member located at said image plane and having a range scale and being yieldingly operably connected to said rotatable member to turn relative to said rotatable member at the ratio l/lc, where k is greater than 1, into angular positions corresponding to the altitudinal angle of said target, the curvature of said spiral guide being defined by the formula r denoting the linear co-ordinate of said spiral guide, o denoting the angular displacement of said rotatable member from a position of origin, lc being a constant greater than 1, n being a con-, stant and he being a constant.

2. In a fire control instrument for anti-aircraft guns, a primary element movable in dependence of varying altitudinal angle of an aerial target, a rotatable member having a spiral guide for displacing said primary element, a turnable multiplying member connected to said primary element and having a rectilinear guide, a secondary element pivotally connected to said multiplying member and movable along said rectilinear guide to be displaced in a predetermined direction in dependence upon angular movements of said multiplying member as well as in dependence upon its movements along said rectilinear guide, an image plane for recording altitudes of the target, a fulcrumed range member located at said image plane and having a range scale and being yieldingly operably connected to said rotatable member to turn relative to said rotatable member at the ratio l/lc, where k is a constant greater than 1, into angular positions corresponding to the altitudinal angle of said target, a stationary abutment for arresting the swing of said range member when attaining a predetermined minimum value a of the altitudinal angle and when the guide member has been turned correspondingly into the position defined by p=k (a.) the curvature of said spiral guide being defined by the formula r=r +h .tan h when (p is greater than a and Sin 0:

-sin

when (p is less than a, r denoting the linear coordinate of said spiral guide, mp denoting the angular displacement of said rotatable member from a position of origin, It being a constant greater than 1, To being a constant and ho being a constant.

ERNST VON SEGEBADEN.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS 

